Belper had the first real chance with skipper Danny South heading over the crossbar after 13 minutes.
The Nailers then hit the post after Curtis Pond spilled the ball and Alex Peterson fired against the upright from a tight angle.
The Scholars best attempt in the first period came when a long ball searched out Josh Cooke but Ryan Musselwhite dashed out quickly from his goal to avert the danger.
Clear cut chances were few and far between and Peterson had a right footed effort stopped by Pond before Musselwhite held a low Jack Langston free kick.
Langston nearly opened the scoring with a drive that deflected off Corey Gregory allowing Musselwhite to scurry across to his left to hold on.
The visitors deservedly took the lead in the 73rd minute. Cooke received the ball outside the box and held off two defenders and curled a low effort off the inside of the post.
Chasetown almost added a second in stoppage time to dent the promotion challenge of the Derbyshire side. Langston was clean through on goal and Musselwhite saved well.